Mathematical Optimization for Data Science Group, Saarland University

Welcome to the homepage of the

Mathematical Optimization for Data Science Group

Department of Mathematics and Computer Science, Saarland University, Germany

Publications

Journal 2025

S. Wang, J. Fadili, P. Ochs:
Inertial Quasi-Newton Methods for Monotone Inclusion: Efficient Resolvent Calculus and Primal-Dual Methods.

SIAM Journal on Imaging Sciences, 18(1):308-344, 2025.

R. Maulen-Soto, J. Fadili, H. Attouch, P. Ochs:
An SDE perspective on stochastic inertial gradient dynamics with time-dependent viscosity and Hessian-driven damping.

Optimization, 0:1-37, 2025.

M. Sucker, J. Fadili, P. Ochs:
Learning-to-Optimize with PAC-Bayesian Guarantees: Theoretical Considerations and Practical Implementation.

Journal of Machine Learning Research (JMLR), 2025.

Conference 2025

S. Mehmood, P. Ochs:
Automatic Differentiation of Optimization Algorithms with Time-Varying Updates.

International Conference on Machine Learning (ICML), 2025.

M. Sucker, P. Ochs:
A Generalization Result for Convergence in Learning-to-Optimize.

International Conference on Machine Learning (ICML), 2025.

C. Castera, P. Ochs:
From Learning to Optimize to Learning Optimization Algorithms.

International Conference on Artificial Intelligence and Statistics (AISTATS), 2025.

Others 2025

S. Wang, J. Fadili, P. Ochs:
Convergence rates of regularized quasi-Newton methods without strong convexity.

Technical Report, ArXiv e-prints, arXiv:2506.00521, 2025.

A. Beck, P. Ochs:
Symmetries in PAC-Bayesian Learning.

Technical Report, ArXiv e-prints, arXiv:2510.17303, 2025.

C. Traoré, P. Ochs:
Bregman Stochastic Proximal Point Algorithm with Variance Reduction.

Technical Report, ArXiv e-prints, arXiv:2510.16655, 2025.

Journal 2024

C. Castera, H. Attouch, J. Fadili, P. Ochs:
Continuous Newton-like Methods featuring Inertia and Variable Mass.

SIAM Journal on Optimization, 34(1):251-277, 2024.

Others 2024

R. Maulen-Soto, J. Fadili, H. Attouch:
Tikhonov Regularization for Stochastic Non-Smooth Convex Optimization in Hilbert Spaces.

Technical Report, ArXiv e-prints, arXiv:2403.06708, 2024.

R. Maulen-Soto, J. Fadili, H. Attouch, P. Ochs:
Stochastic Inertial Dynamics Via Time Scaling and Averaging.

Technical Report, ArXiv e-prints, arXiv:2403.16775, 2024.

M. Sucker, P. Ochs:
A Markovian Model for Learning-to-Optimize.

Technical Report, ArXiv e-prints, arXiv:2408.11629, 2024.

R. Maulen-Soto, J. Fadili, P. Ochs:
Inertial Methods with Viscous and Hessian driven Damping for Non-Convex Optimization.

Technical Report, ArXiv e-prints, arXiv:2407.12518, 2024.

S. Wang, J. Fadili, P. Ochs:
Global non-asymptotic super-linear convergence rates of regularized proximal quasi-Newton methods on non-smooth composite problems.

Technical Report, ArXiv e-prints, arXiv:2410.11676, 2024.

Journal 2023

S. Bonettini, P. Ochs, M. Prato, S. Rebegoldi:
An Abstract Convergence Framework with Application to Inertial Inexact Forward-Backward Methods.

Computational Optimization and Applications, 84:319-362, 2023.

Conference 2023

M. Sucker, P. Ochs:
PAC-Bayesian Learning of Optimization Algorithms.

In F. Ruiz, J. Dy, J-W. van (Eds.): International Conference on Artificial Intelligence and Statistics. Proceedings of Machine Learning Research, Vol. 206, 8145-8164, , 2023.

S. Wang, J. Fadili, P. Ochs:
A Quasi-Newton Primal-Dual Algorithm with Line Search.

International Conference on Scale Space and Variational Methods in Computer Vision (SSVM). Lecture Notes in Computer Science, Springer, 2023.

Others 2023

S. Maier, C. Castera, P. Ochs:
Near-optimal Closed-loop Method via Lyapunov Damping for Convex Optimization.

Technical Report, ArXiv e-prints, arXiv:2311.10053, 2023.

T. Natu, C. Castera, J. Fadili, P. Ochs:
Accelerated Gradient Dynamics on Riemannian Manifolds: Faster Rate and Trajectory Convergence.

Technical Report, ArXiv e-prints, arXiv:2312.06366, 2023.

Journal 2022

M.C. Mukkamala, J. Fadili, P. Ochs:
Global Convergence of Model Function Based Bregman Proximal Minimization Algorithms.

Journal of Global Optimization, 83:753-781, 2022.

Others 2022

S. Mehmood, P. Ochs:
Fixed-Point Automatic Differentiation of Forward--Backward Splitting Algorithms for Partly Smooth Functions.

Technical Report, ArXiv e-prints, arXiv:2208.03107, 2022.

R. Maulen-Soto, J. Fadili, H. Attouch:
An SDE perspective on stochastic convex optimization.

Technical Report, ArXiv e-prints, arXiv:2207.02750, 2022.

Conference 2021

S. Mehmood, P. Ochs:
Differentiating the Value Function by using Convex Duality.

International Conference on Artificial Intelligence and Statistics, 2021.

M.C. Mukkamala, F. Westerkamp, E. Laude, D. Cremers, P. Ochs:
Bregman Proximal Framework for Deep Linear Neural Networks.

International Conference on Scale Space and Variational Methods in Computer Vision (SSVM). Lecture Notes in Computer Science, Springer, 2021.

Journal 2020

E. Laude, P. Ochs, D. Cremers:
Bregman Proximal Mappings and Bregman-Moreau Envelopes under Relative Prox-Regularity.

Journal of Optimization Theory and Applications, 184(3):724-761, 2020.

M.C. Mukkamala, P. Ochs, T. Pock, S. Sabach:
Convex-Concave Backtracking for Inertial Bregman Proximal Gradient Algorithms in Non-Convex Optimization.

SIAM Journal on Mathematics of Data Science, 2(3):658-682, 2020.

Conference 2020

S. Mehmood, P. Ochs:
Automatic Differentiation of Some First-Order Methods in Parametric Optimization.

International Conference on Artificial Intelligence and Statistics, 2020.

Journal 2019

P. Ochs:
Unifying abstract inexact convergence theorems and block coordinate variable metric iPiano.

SIAM Journal on Optimization, 29(1):541-570, 2019.

P. Ochs, T. Pock:
Adaptive Fista for Non-convex Optimization.

SIAM Journal on Optimization, 29(4):2482-2503, 2019.

S. Becker, J. Fadili, P. Ochs:
On Quasi-Newton Forward--Backward Splitting: Proximal Calculus and Convergence.

SIAM Journal on Optimization, 29(4):2445-2481, 2019.

Conference 2019

Y. Malitsky, P. Ochs:
Model Function Based Conditional Gradient Method with Armijo-like Line Search.

In K. Chaudhuri, R. Salakhutdinov (Eds.): International Conference on Machine Learning (ICML). Proceedings of Machine Learning Research, Vol. 97, 4891-4900, PMLR, 2019.

J.A. Tomasson, P. Ochs, J. Weickert:
AFSI: Adaptive restart for fast semi-iterative schemes for convex optimisation.

In T. Brox, A. Bruhn, M. Fritz (Eds.): German Conference on Pattern Recognition (GCPR). Lecture Notes in Computer Science, Vol. 11269, 669-681, Springer, 2019.

M.C. Mukkamala, P. Ochs:
Beyond Alternating Updates for Matrix Factorization with Inertial Bregman Proximal Gradient Algorithms.

Conference on Neural Information Processing Systems (NeurIPS), 2019.

Journal 2018

P. Ochs:
Local Convergence of the Heavy-ball Method and iPiano for Non-convex Optimization.

Journal of Optimization Theory and Applications, 177(1):153-180, 2018.

P. Ochs, J. Fadili, T. Brox:
Non-smooth Non-convex Bregman Minimization: Unification and new Algorithms.

Journal of Optimization Theory and Applications, 181(1):244-278, 2018.

Conference 2018

P. Ochs, T. Meinhardt, L. Leal-Taixe, M. Moeller:
Lifting Layers: Analysis and Applications.

In V. Ferrari, M. Hebert, C. Sminchisescu, Y. Weiss (Eds.): European Conference on Computer Vision (ECCV). Springer International Publishing, 2018. (Oral Presentation at ECCV18)

Journal 2016

P. Ochs, R. Ranftl, T. Brox, T. Pock:
Techniques for gradient based bilevel optimization with nonsmooth lower level problems.

Journal of Mathematical Imaging and Vision, 56(2):175-194, 2016. (Invited Paper)

Conference 2016

S. Müller, P. Ochs, J. Weickert, N. Graf:
Robust interactive multi-label segmentation with an advanced edge detector.

In B. Andres, B. Rosenhahn (Eds.): German Conference on Pattern Recognition (GCPR). Lecture Notes in Computer Science, Vol. 9796, 117-128, Springer, 2016.

D. Hafner, P. Ochs, J. Weickert, M. Reißel, S. Grewenig:
FSI schemes: Fast semi-iterative solvers for PDEs and Optimisation Methods.

In B. Andres, B. Rosenhahn (Eds.): German Conference on Pattern Recognition (GCPR). Lecture Notes in Computer Science, Vol. 9796, 91-102, Springer, 2016. (Best Paper Award)

Journal 2015

P. Ochs, T. Brox, T. Pock:
iPiasco: Inertial Proximal Algorithm for strongly convex Optimization.

Journal of Mathematical Imaging and Vision, 53(2):171-181, 2015.

P. Ochs, A. Dosovitskiy, T. Brox, T. Pock:
On iteratively reweighted algorithms for non-smooth non-convex optimization in computer vision.

SIAM Journal on Imaging Sciences, 8(1):331-372, 2015.

Conference 2015

P. Ochs, R. Ranftl, T. Brox, T. Pock:
Bilevel Optimization with Nonsmooth Lower Level Problems.

In J.-F. Aujol, M. Nikolova, N. Papadakis (Eds.): International Conference on Scale Space and Variational Methods in Computer Vision (SSVM). Lecture Notes in Computer Science, Vol. 9087, 654-665, Springer, 2015. (Best Paper Award)

Others 2015

P. Ochs:
Long Term Motion Analysis for Object Level Grouping and Nonsmooth Optimization Methods.

PhD Thesis, Albert-Ludwigs-Universität Freiburg, 2015.

Journal 2014

P. Ochs, J. Malik, T. Brox:
Segmentation of moving objects by long term video analysis.

IEEE Transactions on Pattern Analysis and Machine Intelligence, 36(6):1187-1200, 2014.

P. Ochs, Y. Chen, T. Brox, T. Pock:
iPiano: Inertial Proximal Algorithm for Non-convex Optimization.

SIAM Journal on Imaging Sciences, 7(2):1388-1419, 2014.

Conference 2013

P. Ochs, A. Dosovitskiy, T. Pock, T. Brox:
An iterated L1 Algorithm for Non-smooth Non-convex Optimization in Computer Vision.

IEEE Conference on Computer Vision and Pattern Recognition (CVPR), 2013.

Journal 2012

M. Temerinac-Ott, O. Ronneberger, P. Ochs, W. Driever, T. Brox, H. Burkhardt:
Multiview deblurring for 3-D images from light sheet based fluorescence microscopy.
IEEE Transactions on Image Processing, 21(4):1863-1873, 2012.

Conference 2012